67035 - Physical Chemistry

Learning outcomes

By the end of the course, students will have acquired the physical and mathematical foundations needed to understand the structure and properties of matter, as well as the physical and chemical transformations involving atoms, molecules, and their states of aggregation.

The course introduces the laws of thermodynamics, which describe energy transformations, and the fundamentals of chemical kinetics, which deal with reaction rates and the factors that affect them.

Finally, the principles of quantum mechanics and their applications will be presented as a coherent framework for understanding the properties of atoms and molecules, the nature of the chemical bond, and molecular spectroscopic properties. The theoretical topics will be complemented by examples, numerical exercises, and practical laboratory activities.

Course contents

Prerequisites

Needed Mathematics Core:

Algebraic, trigonometric, exponential, logarithmic functions. Fundamentals of calculus. Linear differential equations. Principles of Linear Algebra: Matrices, vector spaces, linear transformations.(Attività formativa: Matematica con esercitazioni).

Physics:

Physical quantities and relationships that bind them, main units of measure (Attività formativa: Fisica con esercitazioni).

Chemistry:

Basic chemical principles concerning structure and main properties of the elements, the chemical bond, the molecules and their geometry. Chemical reactions and their balance. (Attività formativa: General and Inorganic Chemistry ).

Topics:

Understanding of the most important physical concepts in mechanics and electromagnetism.(Attività formativa: Fisica con esercitazioni)

Atomic and molecular theory, chemical equations, stiochiometry, problem-solving techniques. (Attività formativa: Chimica Generale e Inorganica con Laboratorio).

The course provides the conceptual and methodological foundations of physical chemistry, with particular emphasis on the thermodynamic and kinetic analysis of chemical processes, as well as on the quantum principles underlying molecular structure and properties. The content is organized into three main modules, in line with the learning objectives of the degree program, and is complemented by practical and numerical exercises aimed at developing applied skills.

I Thermodynamics

Gases: Ideal and Real

• Ideal gas equation of state
• Mixtures of ideal gases and Dalton’s law of partial pressures
• Validity limits of the ideal gas equation
• Real gases: introduction to intermolecular forces
• Real behavior of CO₂ as a function of pressure, temperature, and molar volume
• Critical point and its physical meaning
• Compressibility factor Z and its use to evaluate deviations from ideality
• Virial equation: series expansion for real gases
• Van der Waals equation

Thermodynamic Systems and the First Law

• Thermodynamic systems: open, closed, isolated, adiabatic
• Work and heat as forms of energy transfer
• First law of thermodynamics
• Mechanical work: free expansion, expansion against constant pressure, reversible work
• Heat at constant volume. State functions and exact differentials
• Partial derivatives of internal energy. Heat capacities at constant volume and pressure
• Internal energy and heat capacity of an ideal gas
• Definition and meaning of enthalpy
• Relation between enthalpy, internal energy, and heat at constant pressure
• Isothermal and adiabatic expansions of an ideal gas

Thermochemistry

• Standard enthalpy changes
• Enthalpy of reaction, combustion, and formation
• Temperature dependence of enthalpy: Kirchhoff’s law

Second Law and Entropy; Third Law

• Spontaneous transformations and the second law of thermodynamics
• Entropy: definition and changes in characteristic processes (expansion, heating, phase transitions)
• Third law: absolute entropies
• Reaction entropy and its relation to spontaneity
• Gibbs and Helmholtz free energies and their relation to spontaneity
• Chemical potentials

Gibbs Energy

• Gibbs energy of reaction
• Combination of the first and second laws
• Gibbs–Helmholtz equation
• Dependence of ΔG on temperature and pressure

Thermodynamic Stability and Phase Diagrams

• Criteria for thermodynamic stability
• ΔG dependence and phase transitions
• P–T diagrams of pure substances, triple point and critical point
• Clapeyron and Clausius–Clapeyron equations for phase boundaries

Phases and Solutions

• Gibbs phase rule
• Partial molar quantities: volume and Gibbs energy
• Entropy of mixing. Ideal mixtures and Raoult’s law
• Chemical potential in ideal and real solutions

Colligative Properties

• Vapor pressure lowering. Boiling point elevation and freezing point depression
• Osmotic pressure
• Dilute solutions: Henry’s law

Two-Component Systems

• Liquid–vapor diagrams: P–X and T–X
• Phase localization and the lever rule
• Simple and fractional distillation
• Azeotropes, deviations from Raoult’s law
• T–X diagrams for liquid–liquid and solid–liquid systems
• Eutectic points and compound formation (brief mention)

Chemical Equilibrium

• Extent of reaction, Gibbs energy, and reaction quotient
• Equilibrium constant (Kp, Kc, Kx)
• Activities and standard states
• Effects of temperature and pressure on equilibrium
• Van’t Hoff equation

Electrochemistry

• Galvanic and electrolytic cells. Electrodes, anode and cathode
• Half-reactions and cell potential
• Relationship between ΔG and cell potential
• Nernst equation
• Equilibrium constant and standard potential
• Electrochemical series and temperature dependence
• Ionic activity coefficients. Debye–Hückel limiting law

II Chemical kinetics
Introduction to chemical kinetics. Experimental techniques to study the speed of the reactions. Definition of istantaneous and initial reaction rate. Kinetic laws and order of reaction. Determination of kinetic laws. Method of isolation and method of initial rates. Integrated kinetic law for first order reactions. Half-life for first order reactions. Integrated kinetic laws for second order reactions. Half-life for reactions of second order.

III Quantum mechanics

Introduction to quantum mechanics. Experimental evidence that led to quantum mechanics. De Broglie wavelength. Complex numbers. Operators. Derivation of time-dependent Schrödinger equation for a free particle. Eigenvalues and eigenvectors. Schroedinger equation independent of time. Postulates of quantum mechanics. Particle in a potential well of infinite size. Heisenberg uncertainty principle. Quantum harmonic oscillator. Molecular vibrations. Rigid rotor. Molecular energy levels. Vibro-rotational spectra.

Readings/Bibliography

 

Teaching methods

The course consists of lectures.

In each lecture, the theoretical presentation of the topics included in the programme is accompanied by numerical examples and exercises. The exercises are solved during the lecture by the instructor, with the aim of training students to apply the concepts acquired in the theoretical lectures to the solution of physical chemistry problems. Students are encouraged to participate actively in the solution process by contributing suggestions and reasoning.

When required, thermodynamic data tables from the recommended textbooks are consulted during the solution of exercises.

Assessment methods

The examination consists of a written test and an oral test, held sequentially within the same examination session.

The written test consists of three numerical problems and two open-ended questions. During the written test, students may use only a calculator and a formula sheet, including a copy of the periodic table, made available in advance on Virtuale.

The time allowed for the written test is 120 minutes.

The oral examination, held immediately after the written test, consists of at least two questions on topics covered in the course, including the theoretical aspects of the laboratory component. The minimum overall duration of the oral examination is 45 minutes.

The combined mark for the written and oral tests has a maximum value of 22/30. The examination is passed with a minimum mark of 13/30.

For the final assessment of integrated course unit 67035, namely the present 10-credit course unit, and 67037 Physical Chemistry Laboratory, 6 credits, the assessment methods for course unit 67037 are also taken into account.

Assessment methods for course unit 67037: after each laboratory experiment, each working group must prepare a short report, using the template provided by the instructor, containing only the experimental data. These short reports must be submitted by the following laboratory session or, for the last experiment, within eight days of the activity.

At least 24 hours before the final examination, students must submit, in digital format, Word or PDF, one detailed individual laboratory report on an experiment of their choice, written according to the instructions provided by the instructor during the laboratory course.

The mark for course unit 67037 is based on the overall assessment of the short group reports, maximum 5/30, and of the detailed individual report, maximum 5/30, for a total maximum of 10/30. This mark is added to the mark obtained for course unit 67035.

Please note: the detailed individual report on one laboratory experiment chosen by the student must be submitted before the examination. If it is not submitted, the assessment of the laboratory component will be based only on the short group reports.

 

For learning assessment purposes, limited, declared and non-substantial use of AI is permitted for support activities, such as summarising or rephrasing. Substantial use of AI to complete parts of the examination is not allowed.

Students with specific learning disorders and/or temporary or permanent disabilities should contact the relevant University office in good time. The office will propose any appropriate adjustments, which must in any case be submitted to the instructor for approval at least 15 days before the examination date. The instructor will assess their suitability also in relation to the learning objectives of the course unit.

Office hours

See the website of Elisabetta Venuti

See the website of Riccardo Tarroni